Problem: The value of $\sqrt{77}$ lies between which two consecutive integers ? Integers that appear in order when counting, for example 2 and 3.
Consider the perfect squares near $77$ . [ What are perfect squares? Perfect squares are integers which can be obtained by squaring an integer. The first 13 perfect squares are: $ 1,4,9,16,25,36,49,64,81,100,121,144,169$ $64$ is the nearest perfect square less than $77$ $81$ is the nearest perfect square more than $77$ So, we know $64 < 77 < 81$ So, $\sqrt{64} < \sqrt{77} < \sqrt{81}$ So $\sqrt{77}$ is between $8$ and $9$.